Holonomy and vortex structures in quantum hydrodynamics
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911254288793600 |
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| author | Foskett, Michael S. Tronci, Cesare |
| author_facet | Foskett, Michael S. Tronci, Cesare |
| contents | We consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. In particular, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero holonomy. In the hydrodynamic context, this leads to a fluid velocity which no longer is constrained to be irrotational and allows instead for vortex filaments solutions. After exploiting the Rasetti-Regge method to couple the Schrödinger equation to vortex filament dynamics, the latter is then considered as a source of geometric phase in the context of Born-Oppenheimer molecular dynamics. Similarly, we consider the Pauli equation for the motion of spin particles in electromagnetic fields and we exploit its underlying hydrodynamic picture to include vortex dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_08664 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Holonomy and vortex structures in quantum hydrodynamics Foskett, Michael S. Tronci, Cesare Mathematical Physics Chemical Physics Quantum Physics We consider a new geometric approach to Madelung's quantum hydrodynamics (QHD) based on the theory of gauge connections. In particular, our treatment comprises a constant curvature thereby endowing QHD with intrinsic non-zero holonomy. In the hydrodynamic context, this leads to a fluid velocity which no longer is constrained to be irrotational and allows instead for vortex filaments solutions. After exploiting the Rasetti-Regge method to couple the Schrödinger equation to vortex filament dynamics, the latter is then considered as a source of geometric phase in the context of Born-Oppenheimer molecular dynamics. Similarly, we consider the Pauli equation for the motion of spin particles in electromagnetic fields and we exploit its underlying hydrodynamic picture to include vortex dynamics. |
| title | Holonomy and vortex structures in quantum hydrodynamics |
| topic | Mathematical Physics Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2003.08664 |